Question

已知如图,抛物线y=ax2+bx+c(a>0)的对称轴为直线x=-1·····

Answer 1

A(x1,0),B(x2,0)

0 < x1 < 1 (i)

1 < x1 - (-1) < 2,(-1为对称轴)

同理,1 < -1 - x2 < 2,2 < -x2 < 3 (ii)

二者相乘,0 < -x1*x2 < 3,0 < -ax1*x2 < 3a (a > 0)

y = a(x - x1)(x - x2)

x = 0,y = c = ax1*x2

-c = -ax1*x2

0 < -c < 3a

即3a + c > 0